MATH 126 Final: MATH 126 UW Final Exam Winter 2009 Solutions
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, 5(cid:19: (2, 2) and ( 2, 2, the minimum speed is 3 feet per second. 4. (a) t2(x) = 1 + 2(x 1) + 3 (b) f (0. 8) 0. 66 (c) one acceptable answer is |f (x) t2(x)| 4. 2 (x 1)2 with the appropriate work. ) 5. (a) the taylor series for f (x) based at b = 0 is: Xk=0 ( 1)k3k+1 ek+1(k + 1) xk+1. (b) the series converges for |x| < e. 3 . (a) x = t, y = 1, z = + 2t (b) y = 1. 7. (a) the domain is all points on and inside the circle centered at (e, e) with radius 5e that lie above the line y = x. (b) . 8. (a) here"s what d looks like: (b) 2 . 3 + 3: there is a saddle point at (0, 0) and a local minimum at (cid:18) 9.
